Convert Gradians to Seconds of Arc
Gradian (grad) to Second of Arc (") unit conversion — enter any value below to get an instant result, or use the table for common values.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
1 grad = 3239.9997 "
1 Gradian = 3239.9997 Seconds of Arc
1 Second of Arc = 0.000308642 Gradians
1 grad in every supported unit
Conversion chart: Gradian to Seconds of Arc
Conversion table
| Gradian (grad) | Second of Arc (") |
|---|---|
| 0.01 grad | 32.399997 " |
| 0.1 grad | 323.99997 " |
| 1 grad | 3239.9997 " |
| 2 grad | 6479.9995 " |
| 3 grad | 9719.9992 " |
| 5 grad | 16199.999 " |
| 10 grad | 32399.997 " |
| 20 grad | 64799.995 " |
| 50 grad | 161999.99 " |
| 100 grad | 323999.97 " |
| 1000 grad | 3239999.7 " |
Gradian (grad)
Definition: One 400th of a full circle, a metric-inspired angle unit designed so a right angle equals exactly 100 gradians.
History: Introduced alongside the metric system during the French Revolution as the "grade," intended to bring decimal simplicity to angle measurement the same way meters brought it to length.
Current use: Still used in surveying and some European civil engineering and artillery contexts, particularly where decimal subdivisions of a right angle are convenient.
Second of Arc (")
Definition: One 60th of an arcminute, and therefore one 3,600th of a degree — an extremely fine unit of angular measurement.
History: Like the arcminute, it descends from the ancient Babylonian base-60 system, extended a second level deeper the same way a minute of time divides into 60 seconds.
Current use: Used in astronomy to measure star positions, parallax, and telescope resolution, where even a tiny fraction of a degree represents a meaningful difference.
Supported Units
| Unit | Symbol | In Degrees |
|---|---|---|
| Degree | ° | 1 ° |
| Radian | rad | 57.29578 ° |
| Gradian | grad | 0.9 ° |
| Minute of Arc | ' | 0.016666667 ° |
| Second of Arc | " | 0.0002777778 ° |
| Revolution | r | 360 ° |
| Quadrant | quad | 90 ° |
| Sextant | sext | 60 ° |
| Mil (angular) | mil | 0.05625 ° |
| Sign (zodiac) | sign | 30 ° |
About These Parameters
- Value
- The number you want to convert, expressed in the "From" unit. Accepts decimals.
- From Unit
- The unit your input angle is currently measured in.
- To Unit
- The unit you want the result converted into. Use the swap button to flip From and To instantly.
How Angle Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the degree. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Gradian → Second of Arc: multiply by 3239.9997. For example, 1 grad × 3239.9997 = 3239.9997 ".
Why Radians Are the Natural Unit
In calculus and physics, the radian is the unit angles are "supposed" to be measured in, because it removes an awkward conversion constant from the math. If an angle is measured in radians, the length of the arc it traces on a circle is simply the radius multiplied by the angle (arc length = radius × angle in radians) — no factor of π/180 required. That same clean relationship is why derivatives and integrals of trigonometric functions only take their simple, familiar forms when the angle is in radians; measuring in degrees would scatter conversion constants throughout every formula.
The 360-Degree Circle: A Babylonian Legacy
Dividing a circle into 360 degrees dates back roughly 4,000 years to Babylonian astronomers, who counted using a base-60 (sexagesimal) number system rather than the base-10 system most of the world uses today. 360 is convenient in base-60 because it divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, and many other numbers, and it sits close to the roughly 365-day length of a solar year used in early calendars. That ancient choice survived the fall of Babylon and traveled through Greek and Islamic astronomy into the modern world, which is why circles still split into 360 parts instead of a rounder base-10 number like 100 or 1,000.
Example
1 grad equals 3239.9997 ". For scale, that's about 0.01× a right angle (90°, or 100 grad) — a half turn of 180° works out to π radians, and a full turn of 360° works out to 2π radians.
Frequently Asked Questions
How many Seconds of Arc are in 1 Gradian?
1 Gradian (grad) equals exactly 3239.9997 Seconds of Arc (").
Why does a circle have 360 degrees?
The 360-degree circle comes from ancient Babylonian astronomers, who used a base-60 counting system and a roughly 365-day calendar year; 360 divides evenly by many small numbers, which made it a practical choice for hand calculation long before calculators existed, and the convention simply stuck through Greek and later Western science.
What is a radian in plain terms?
A radian is the angle you get when you wrap a circle's radius along its own edge — the arc traced out is exactly as long as the radius. That works out to about 57.3 degrees, and it's the unit that makes calculus formulas involving circles and rotation come out clean and simple.
How accurate are these conversions?
Every conversion factor used here is an exact, mathematically defined relationship (for example, 1 radian = exactly 180/π degrees) — results are limited only by floating-point display precision, not by rounded conversion constants.